最佳化設計以有系統的方式，找尋拘束空間內目標函數的最大或最小值，這樣的最佳解雖可使設計工程師了解產品的極致性能表現，但也時常位於拘束條件邊界上。任何工程問題上的不確定因素，均很可能導致最佳值滿足拘束條件的可靠度偏低。可靠度最佳化設計便是一個在設計初期便考量不確定因素的設計方法，其嚴謹卻實用的數學模式在工程領域被廣泛的應用。在過去大多數的研究中，都是在設定一個固定的可靠度作為拘束條件來進行設計，然而對於一個未知的問題來說，訂定一個不適當的可靠度機率值，將有可能會導致問題的可行解空間並不存在，或是高估了問題本身所能要求的可靠度。因此，本論文將使用Efficient Global Optimization(EGO) 演算法，在機率形式的拘束條件下，以最大可靠度作為目標來進行最佳化設計。

EGO演算法使用本論文所提出的取樣指標，結合其他文獻中舊有的指標，制定一個探索式的方法來不斷地在拘束條件邊界上取樣，以改善由蒙地卡羅法所計算的拘束條件之準確性，並建立Kriging模型來對各個不連續的可行解空間，進行最大可靠度的全域最佳化設計。由本論文之結果可以得知，在針對黑盒子函數問題與非連續可行解空間的可靠度問題中，此方法將比梯度型演算法或DIRECT演算法來的有效率。文末將以兩個數學範例與一個工程範例來說明演算法之結果。

Design optimization problems under random uncertainties are commonly formulated with constraints in probabilistic forms. This formulation is also referred to as reliability-based design optimization (RBDO) in the literature and has gained extensive attentions in recent years. Most research assumes that reliability levels are given based on past experiences or other design considerations without exploring the constrained space. As a result, inappropriate target reliability levels might be assigned, which either result in null probabilistic feasible space or performances underestimation. In this research we investigate the maximal reliability withnin a probabilistic constrained space using modified efficient global optimization (EGO) algorithm. By constructing and improving Kriging models iteratively, EGO can obtain a global optimum of a possibly disconnected feasible space at high reliability levels. An infill sampling criterion (ISC) is proposed to enforce added samples on constraint boundaries to engance the accuracy of probabilistic constraint evaluations via Monte Carlo simulation. This limit state ISC, combined with existing ISC from the literature, forms a heuristic approach that efficiently improves the Kriging models. For optimization problems with expensive functions and disconnected feasible space, such as the maximal reliability problems in RBDO, the proposed work shows high efficiency and potential in finding the optimum compared to existing gradient-based and direct search methods. Several examples are used to demonstrate the proposed methodoogy.

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